Men experience significantly lower rates of most common mental disorders; that gap is wider in younger people, appears to be widening over time and persists after controlling for confounding variables. Men are more likely to die by suicide, but they're drastically less likely to attempt suicide; the discrepancy is accounted for by men choosing more lethal means.

There is simply no evidence to support the idea that women are better at coping with psychological distress, or that men would benefit from adopting stereotypically female coping strategies.